No, I don't remember having signed up for the Product Improvement Program. So I went and ran a little test: I launched LR, allowed the first "phone home," went to the help menu and examined the APIP dialog (no clue there), deliberately checked "NO" and quit. No closing request. Relaunched LR, and guess what? No initial request, either. So I returned to the APIP dialog, still no clues as to what had been checked earlier, this time clicked yes, saw that the "what are you" dialog was already filled out (so maybe I HAD said yes to APIP earlier?), and then quit LR. This time there WAS a closing request.
So, I think the mystery is solved: these are connected to the APIP program. One does wonder, however, if APIP is primed to assume your participation. As I think about it, I may very well have agreed to participate in a dialog that opened when I first launched the beta version. (Why else HAVE a public beta?) Since there are a couple Product Improvments I'd like to see, I think I need to tell Li'l Snitch to allow those connections in future.
Thank you, @Jim01403, for solving the riddle.
